Abstract

We propose a method for mutual fund performance measurement and best-practice benchmarking, which endogenously identifies a dominating benchmark portfolio for each evaluated mutual fund. Dominating benchmarks provide information about efficiency improvement potential as well as portfolio strategies for achieving them. Portfolio diversification possibilities are accounts for by using Data Envelopment Analysis (DEA). Portfolio risk is accounted for in terms of the full return distribution by utilizing Stochastic Dominance (SD) criteria. The approach is illustrated by an application to US based environmentally responsible mutual funds.

Keywords

This paper has benefited of helpful comments from Thierry Post, two anonymous reviewers, and participants in the CEMMAP workshop “Testing Stochastic Dominance Restrictions”, November 2005, London UK; 4th International DEA Symposium, September 2004, Birmingham UK; the VIII European Workshop of Efficiency and Productivity Analysis, September 2003, Oviedo, Spain; and the EURO/INFORMS joint international meeting, July 2003, Istanbul, Turkey. The usual disclaimer applies.

JEL Classifications

Appendix: Why imposing risk aversion by assumption does not influence the efficiency measure when the evaluated portfolio has relatively low risk

In Sect. 4 we found that all eight environmentally responsible mutual funds scored equally well in terms of FSD and SSD efficiency. The aim of this appendix is to try to rationalize this finding by means of a stylized graphical example.

Figure A presents a two-dimensional case where state 1 represents a bear market and state 2 a bull market. A risk-free asset is displayed in the bottom-right corner of the diagram; the broken diagonal line that runs through the risk free asset indicates vectors that yield equal return in both states. Volatile reference stocks are typically found in the top-left corner of the diagram, where return is negative in state 1, and highly positive in state 2. The evaluated mutual fund lies somewhere between the benchmark stock and the risk-free asset, within the return possibility set; this set is indicated by the thick solid piece-wise linear frontier with vertices in the risk-free asset and the reference stocks. The set of return vectors that dominate the evaluated fund by SSD (i.e., “the SSD dominating set”, see Kuosmanen 2004) is indicated by the thin piece-wise linear isoquant that runs through the evaluated fund. This dominating set overlaps with the return possibilities set, and thus fund 0 is SSD inefficient.

Note that the mean return of the reference stocks must typically be higher than the return of the risk-free asset, to compensate for the higher risk. Thus, the slope of the return possibilities frontier must generally be steeper than that of diagonal line-segment of the SSD dominating set, like in Fig. 1. Recall that the PK measure selects the benchmark portfolio from the intersection of the return possibility set and the SSD dominating set by maximizing the difference in mean return between the benchmark portfolio and the evaluated fund. In this example, the benchmark portfolio will be found directly above the point representing the return vector of the mutual fund 0, as indicated in Fig. A. Note that this benchmark is also included in the FSD dominating set. Thus, exactly the same benchmark is obtained by using the FSD criterion. (A similar argument holds for the DD measure.)

Although this stylized example involves only two states, it does describe some essential features of the phenomenon at hand. Also in the general setting with S states of nature, the maximum mean return over the intersection of the return possibility set and the SSD dominating set is usually found in the corner point where the boundaries of the return possibility set and the SSD dominating set intersect. The FSD and SSD measures will differ when there exists an asset that offers a high mean return with a low risk, or if the evaluated mutual fund itself is highly risky. Given the usual geometry of the return possibilities sets, the FSD and SSD measures are likely to yield the same results in the efficiency assessment of the mutual funds and other well-diversified portfolios such as the market portfolio.